In conventional communication receivers, data symbol detection and channel decoding are performed separately. Recently, iterative detection and decoding (IDD) receivers are introduced to improve the receiver performance. The IDD receiver performs symbol detection and channel decoding iteratively by exchanging soft information that may be expressed in the form of log likelihood ratio (LLR). To realize such IDD receivers, both the symbol detector and the decoder may be implemented in a soft-input soft-output fashion.
While there exists well known low-complexity soft-in soft-out channel decoding algorithms such as max-log-MAP (maximum a posteriori) decoder, implementation of symbol detectors is challenging due to high computational complexity especially for large systems (e.g., MIMO systems with many antennas). For example, complexity of the optimal soft-input soft-output symbol detector (e.g., a posteriori probability (APP) detector) grows exponentially in terms of the size of symbol vector and modulation order. Although there are linear low-complexity symbol detectors such as a linear minimum mean square error (MMSE) detector aiming to reduce the complexity, the performance gap of the linear detectors from the APP detector is known to be nontrivial.